You bought Windows 7 Home Premium Family 3 pack Upgrade version?
That's retail Windows 7 which means you can reinstall it as often as you want for life, as long as it is only on 3 machines at a time.
Just remember you need a qualifying XP or Vista OS which either came with each upgraded machine, or a retail XP/Vista you own and do not use again during the time it is being used to qualify for Upgrade version for each upgraded machine.
The qualifying OS does not have to be installed on the machine at the time you Upgrade: Clean Install with a Upgrade Windows 7 Version
These are provisions of the EULA, enforced on the honor system.